Starting small: exploring the origins of successor function knowledge. Issue 4 (2nd March 2021) - Schneider, Rose M.; Pankonin, Ashlie; Schachner, Adena; Barner, David
Abstract: Although most U. S. children can accurately count sets by 4 years of age, many fail to understand the structural analogy between counting and number — that adding 1 to a set corresponds to counting up 1 word in the count list. While children are theorized to establish this Structure Mapping coincident with learning how counting is used to generate sets, they initially have an item‐based understanding of this relationship, and can infer that, e.g, adding 1 to "five" is "six", while failing to infer that, e.g., adding 1 to "twenty‐five" is "twenty‐six" despite being able to recite these numbers when counting aloud. The item‐specific nature of children's successes in reasoning about the relationship between changes in cardinality and the count list raises the possibility that such a Structure Mapping emerges later in development, and that this ability does not initially depend on learning to count. We test this hypothesis in two experiments and find evidence that children can perform item‐based addition operations before they become competent counters. Even after children learn to count, we find that their ability to perform addition operations remains item‐based and restricted to very small numbers, rather than drawing on generalized knowledge of how the count list represents number. We discuss how these early item‐based associations between number words and sets might play a role in constructing a generalized Structure Mapping between counting and quantity. Abstract : Previous research has found that young children are unable to numerically label the output of addition operations with +1 until they acquire the Cardinal Principle (CP), which is typically taken as evidence that acquiring the CP entails the establishment of a Structure Mapping between counting and cardinality. However, CP‐knowers' ability to perform +1 addition operations is initially item‐specific, suggesting it may instead reflect Associative Mappings drawn between set representations and known number words, and that children do not establish a Structure Mapping between counting and cardinality until later in development. We find evidence for this Associative Mapping hypothesis by showing that 2‐ to 4‐year‐old CP‐ and subset‐knowers' ability to compute +1 addition operations for a range of small and familiar numbers (1‐5) is related to their knowledge of number words, rather than counting.